A patch algorithm for fast registration of distortions

This note describes an algorithm for registration of non-linear distortions in two-dimensional (2D) images. The algorithm solves an integrated form of linearized image matching equation over a set of patches in the image domain. The distortion field is represented as a linear combination of multinomials in the image-plane coordinates. Prior to registration, the images are convolved with band-pass filters that are implemented at a coarse-to-fine hierarchy of spatial scales (specified at input by the user); and some heuristics are given for choosing these scales. Images registered at a coarse scale are used as input approximations for deriving images registered at a subsequent finer scale of resolution. With this prescribed hierarchy, the algorithm is non-iterative; it is also robust to noise, and can in principle accommodate arbitrary local or global distortions. The results indicate that non-linear registration does improve the match between images.